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Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

Part of: Collisions in Collisionless Plasmas

Published online by Cambridge University Press:  05 September 2014

A. Kanekar ,
A. A. Schekochihin ,
W. Dorland  and
N. F. Loureiro
A. Kanekar*
Affiliation:
Department of Physics, University of Maryland, College Park, MD 20742-3511, USA
A. A. Schekochihin
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK
W. Dorland
Affiliation:
Department of Physics, University of Maryland, College Park, MD 20742-3511, USA
N. F. Loureiro
Affiliation:
Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
*
†Email address for correspondence: anjor@umd.edu
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Abstract

A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard “fluid” one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 305810104
Copyright
Copyright © Cambridge University Press 2014 

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